Types of matrices
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Definition.
A square matrix is a matrix in which the number of rows equals the number of columns (size n×n), the number n, is called the order of the matrix.Example.
4  1  7   a square matrix with size 3×3  
1  0  2  
4  6  7 
Definition.
The zero matrix is a matrix whose entries are equal to zero, ie, a_{ij} = 0, ∀i, j.Example.
0  0  0   zero matrix  
0  0  0 
Definition.
Row vector is a matrix consisting of a one row.Example.
1  4  5   row vector 
Definition.
Column vector is a matrix consisting of a one column.Example.
8   column vector  
7  
3 
Definition.
Diagonal matrix is a square matrix whose entries standing outside the main diagonal are equal zero.Example of diagonal matrix.
4  0  0   diagonal entries are arbitrarynot diagonal entries are equal to zero  
0  5  0  
0  0  0 
Definition.
Identity matrix is a diagonal matrix in which all the elements on the main diagonal are equal to 1.Denote.
The identity matrix usually denoted by I.Example of identity matrix.
I =  1  0  0   diagonal entries are equal to 1not diagonal entries are equal to 0  
0  1  0  
0  0  1 
Definition.
Upper triangular matrix is a matrix whose elements below the main diagonal are equal to zero.Example of upper triangular matrix.
7  6  0  
0  1  6  
0  0  0 
Definition.
Lower triangular matrix is a matrix whose elements above the main diagonal are equal to zero.Example of lower triangular matrix.
7  0  0  
6  1  0  
2  0  5 
N.B. The diagonal matrix is a matrix that is both upper triangular and lower triangular.
Definition.
Specifically, a matrix is in row echelon form if:
 all nonzero rows are above all zero rows;
 if the first nonzero element of a row is located in a column with the number i, and the next line is not zero, then the first nonzero element of the next line should be in the column with number greater than i.
Examples of row echelon form of matrix.


MatrixMatrix Definition. Main informationSystem of linear equations  matrix formTypes of matricesMatrix scalar multiplicationAddition and subtraction of matricesMatrix multiplicationTranspose matrixElementary matrix operationsDeterminant of a matrixMinors and cofactors of a matrixInverse matrixLinearly dependent and independent rowsRank of a matrix
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